Basepoint estimator

ABSTRACT

A method of estimating a basepoint includes receiving a plurality of goals, wherein each goal has a desired value, and receiving a plurality of sensor feedback signals from a controlled system. A plurality of predicted output values of the controlled system are received from a mathematical model. A desired change for a plurality of basepoint values is estimated in response to the goals, the feedback, and the predicted output values. An actual change in basepoint values is calculated in response to a plurality of limits and the desired change for the plurality of basepoint values according to a plurality of goal weights while holding limits. The actual change in basepoint values is combined with last pass values of the plurality of basepoint values to produce an updated basepoint estimate.

This invention was made with government support under Contract No.N00019-02-C-3003 awarded by the United States Navy. The government maytherefore have certain rights in this invention.

BACKGROUND OF THE INVENTION

This application relates to control systems, and more particularly to amethod of estimating a basepoint in a multivariable control systemaccording to a relative goal prioritization scheme.

In control theory, a given control system may have a plurality of goalsand a plurality of limits. Limits are inequality constraints on systemdynamic variables. An example limit may be to prevent an enginetemperature from exceeding a certain temperature to prevent enginedeterioration. An example goal may be to achieve a certain engine thrustlevel, such as a thrust of 10,000 pounds. While it is desirable toachieve goals, it is necessary to meet limits.

A multivariable system may include a number of effectors that can beadjusted to meet system goals and limits. In some cases, a system may becross-coupled, which means that each effector change may affect goalsand limits with varying dynamics. In a cross-coupled system, it may notbe possible to change a single effector in isolation to affect a singlegoal or limit, as a change in one effector may affect a plurality ofgoals or limits.

A basepoint is a set of system values corresponding to a state ofequilibrium in which a rate of change for the system is zero, apredetermined amount of limits are met, and a quantity of goals arefulfilled.

SUMMARY OF THE INVENTION

A method of estimating a basepoint includes receiving a plurality ofgoals, wherein each goal has a desired value, and receiving a pluralityof sensor feedback signals from a controlled system. A plurality ofpredicted output values of the controlled system are received from amathematical model. A desired change for a plurality of basepoint valuesis estimated in response to the goals, the feedback, and the predictedoutput values. An actual change in basepoint values is calculated inresponse to a plurality of limits and the desired change for theplurality of basepoint values according to a plurality of goal weightswhile holding limits. The actual change in basepoint values is combinedwith last pass values of the plurality of basepoint values to produce anupdated basepoint estimate.

These and other features of the present invention can be best understoodfrom the following specification and drawings, the following of which isa brief description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example multivariable controlsystem.

FIG. 2 schematically illustrates a basepoint estimator that could beused in the multivariable control system of FIG. 1.

FIG. 3 schematically illustrates another basepoint estimator that couldbe used in the multivariable control system of FIG. 1.

FIG. 4 schematically illustrates a quadratic problem solver from thebasepoint estimator of FIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 schematically illustrates an example multivariable control system10. The system 10 includes a basepoint estimator 16 operable to receivea plurality of goals 12 (“yref”), a plurality of maximum limits 14(“ymax”), a feedback signal 28 (“yfb”), and a predicted output 19 (“ŷ”)from a mathematical model 22, and is operable to calculate a basepointestimate 20 in response to the goals 12, limits 14, feedback signal 28,and model predictions 19. It is understood that the feedback signal 28could include a plurality of feedback signals. The model predictions 19correspond to predicted behavior of a controlled system 32, include anassociated entry for the feedback signal 28 (or if there are a pluralityof feedback signals, include an associated entry for each of theplurality of feedback signals), and may include additional variables notassociated with a feedback sensor. A basepoint is a set of valuescorresponding to an equilibrium point at which a rate of change of thecontrolled system 32 is zero, and at which a predetermined amount oflimits 14 are met and a quantity of goals 12 are fulfilled according toa goal prioritization scheme.

One embodiment of a multivariable control system 10 is described incommonly-assigned, co-pending U.S. application Ser. No. 12/115,574, thedisclosure of which is incorporated herein by reference.

The basepoint estimate 20 is transmitted to the mathematical model 22and to control logic 24. In one example, the mathematical model 22 is atime varying linear model, such as a quasi-linear parameter varying(“QLPV”) model. The basepoint estimate 20 includes a change in anestimated state 42 (“Δ{circumflex over (x)}”) of the controlled system32, internal reference values 44 (“yr”), free basepoint values 46(“{circumflex over (b)}pf”) that do not have reference values, andbasepoint values 48 (“ŷcb”) associated with variables having limits.Throughout this application a carat (“^”) corresponds to an estimatedvalue.

The control logic 24 receives the basepoint estimate 20 and producesactuator requests 30 (“urq”), which are transmitted to the controlledsystem 32 to effect change in the controlled system 32. In one examplethe controlled system 32 is a vehicle, such as an aircraft. However, itis understood that the multivariable control system 10 could be used tocontrol other systems. The transmission of actuator requests 30 to thecontrolled system 32 may include transmitting the actuator requests 30to actuators which control effectors that may be adjusted to control thecontrolled system 32. The feedback signal 28 is transmitted from thecontrolled system 32 back to the multivariable control system 10. Thebasepoint estimator 16, basepoint estimate 20, other control logic 24,actuator requests 30, QLPV model 22, and predicted output 19 (“ŷ”)collectively form an estimator loop.

The mathematical model 22 may be based on equations #1-2, as shownbelow:x _(n+1) =A(p)*(x _(n) −xb _(n))+B(p)*(urq _(n) −ub _(n))+xb_(n)  equation #1y _(n) =C(p)*(x _(n) −xb _(n))+D(p)*(urq _(n) −ub _(n))+yb_(nn)  equation #2

where xb_(n), ub_(n), and yb_(nn) are basepoint values;

x corresponds to the state of the controlled system 32;

y_(n) corresponds to outputs of the controlled system 32;

urq_(n) corresponds to actuator requests;

p corresponds to parameters; and

A, B, C, and D are coefficients.

In the basepoint estimator 16, the collection of basepoints in thevectors xb, ub, and yb are regrouped into vectors yr, bpf, and ycb,where yr corresponds to basepoints for variables for which there areassociated desired values (or “goals”), ycb corresponds to basepointsfor variables for which there are limits, and bpf is a vector containingthe remaining basepoints (or “free basepoints”).

FIG. 2 schematically illustrates a basepoint estimator 16 a that couldbe used in the multivariable control system 10 of FIG. 1. The basepointestimator 16 a is simplified in that it does not hold limits. Thebasepoint estimator 16 a is operable to calculate a model predictionerror 50 (“{tilde over (y)}”) in response to the feedback signal 28 andthe model predictions 19. An estimator module 60 calculates the changein the estimated system state 42, a desired change in free basepointvalues 62 (“Δ{circumflex over (b)}pf 1”), and a desired change inbasepoint values associated with variables having limits 64 (“Δŷcb1”) inresponse to the model prediction error 50. The desired changes 62, 64are combined to form a desired change in basepoint values 66 (“x_bpe”)vector.

Identity matrix 68 a sets an actual change in basepoint values 70 (“x2”)equal to the desired change in basepoint values 66. Identity matrix 68 bsets reference values 44 equal to goals 12. The identity matrices 68 aand 68 b are used because FIG. 2 illustrates a simplified basepointestimator 16. It is understood that identity matrices may not be able tobe used in certain cases, such as when limits are active in thecontrolled system 32.

The actual change in basepoint values 70 is processed with a prioribasepoint values 46 a (“ bpf”) and 48 a (“ ycb”) to estimate basepointvalues 46 (“{circumflex over (b)}pf”) and 48 (“ŷcb”). Throughout thisapplication, a line above a variable indicates an a priori estimate ofthat variable. For example, “ x” would correspond to an a priori valueof x. A processing step 72 a (“z⁻¹”) indicates that a value from aprevious iteration, or a “last pass value”, is used to produce a newvalue. One of ordinary skill in the art would understand how to performsuch a processing step.

FIG. 3 schematically illustrates a basepoint estimator 16 b that isoperable to handle active limits. A quadratic programming (“QP”) solvermodule 74 is used to calculate the actual change in basepoint values 70(“x2”) in response to the desired change in basepoint values 66, amathematical model matrix 76 (“CE”), a mathematical model matrix 78(“J”), and processed limits 80 (“K”). The matrices 76 and 78 may becalculated according to equations 3-10 shown below.

$\begin{matrix}{{CE} = \begin{bmatrix}I & 0 & 0 \\{{CE}\; 1} & {{CE}\; 2} & {{CE}\; 3}\end{bmatrix}} & {{equation}\mspace{14mu}\#\; 3} \\{{CE} \equiv \frac{\partial\hat{y}}{{\partial y}\; r}} & {{equation}\mspace{14mu}\#\; 4} \\{{{CE}\; 2} \equiv \frac{\partial\hat{y}}{\partial{bpf}}} & {{equation}\mspace{14mu}\#\; 5} \\{{{CE}\; 3} \equiv \frac{\partial\hat{y}}{\partial{ycb}}} & {{equation}\mspace{14mu}\#\; 6} \\{J = \left\lbrack {J\; 1\mspace{14mu} J\; 2\mspace{14mu} J\; 3} \right\rbrack} & {{equation}\mspace{14mu}\#\; 7} \\{{J\; 1} \equiv {{\frac{{\partial\hat{y}}c}{\partial\hat{y}} \cdot {CE}}\; 1}} & {{equation}\mspace{14mu}\#\; 8} \\{{J\; 2} \equiv {{\frac{{\partial\hat{y}}c}{\partial\hat{y}} \cdot {CE}}\; 2}} & {{equation}\mspace{14mu}\#\; 9} \\{{J\; 3} \equiv {{\frac{{\partial\hat{y}}c}{\partial\hat{y}} \cdot {CE}}\; 3}} & {{equation}\mspace{14mu}\#\; 10}\end{matrix}$

where ŷc corresponds to a portion of 9 that has corresponding limitedvariables.

The basepoint estimator 16 b is operable to calculate a differencebetween the goals 12 and a last pass value (see processing step 72 b) ofreference values 44 to determine nominal goal changes 82 (“Δyr_nom”).The nominal goal changes 82 are included in the desired change inbasepoint values 66. A first gain matrix 84 (“gref”) may be used toprovide a smooth transition off a limit. For example, if a limit wasactive, and was then found to be inactive, the gain matrix 84 couldprovide a smooth transition off the limit so that the controlled system32 does not experience an abrupt change.

The basepoint estimator 16 b is also operable to calculate a differencebetween the plurality of limits 14 and a last pass value (see processingstep 72 c) of basepoint values 48 (“ŷcb”) to determine a remaining datarange 86 (“yc_(available)”) until a limit is active. Those with ordinaryskill in the art could also replace ŷcb, the anticipated value of thelimited variable at equilibrium in signal 48, with ŷc, the prediction ofthe dynamically changing value of the limited variable from themathematical model 22. A second gain matrix 88 (“glim”) may be appliedto the remaining data range 86 to produce processed limits 80 (“K”). Thesecond gain matrix 88 can facilitate a smooth transition onto a limit,so that the controlled system 32 system may asymptotically reach a limitand not abruptly hit the limit.

In the example of FIG. 3, actual change in basepoint values 70 (“x2”) isa vector that includes actual changes in perturbations to yr, bpf, andycb. These perturbations are added to the a priori basepoint values 46 a(“ bpf”) and 48 a (“ ycb”) and to goal reference values 12 (“yref”) toform updated values for internal reference vales 44 (“yr”), andbasepoint values 46 (“{circumflex over (b)}pf”) and 48 (“ŷcb”).

FIG. 4 schematically illustrates the QP solver 74 of FIG. 3 in greaterdetail. FIG. 4 is an example of how one might solve the QP problemactive set algorithm using a big-K approach to tolerating infeasiblestarting points. If a limit or a plurality of limits are active, themultivariable control system 10 may change the behavior of thecontrolled system 32 to avoid exceeding the active limits. To achievethis, the QP solver module 74 chooses the actual change in basepointvalues 70 (“x2”) to minimize a performance index (“PI”), represented byequation #11 below, subject to the constraints shown in equations #12-14below. Equations #15-16 indicate a notation that may be used for the PIand the constraints.

$\begin{matrix}{{PI} = {{\frac{1}{2}{\left( {{\Delta\;{yr}} - {\Delta\;{yr\_ nom}}} \right)_{n + 1}}_{Q}^{2}} + {\frac{1}{2}{{x\; 2_{n}}}_{R}^{2}}}} & {{equation}\mspace{14mu}\#\; 11}\end{matrix}$

where Q corresponds to goal-weighting matrix 96; and

R corresponds to x2-weighting matrix 97.J·x2≦K≡g lim·(Y max−ŷcb _(n))  equation #12Δyr ₁₃ nom=gref·(yref−yr)_(n) +Δyref _(n+1)  equation #13[C1 C2 C3]·x2=[C1 C2 C3]·x _(—) bpe  equation #14∥x∥ _(Q) ² =x ^(T) Q·x  equation #15Δ( )_(n+1)≡( )_(n+1)−( )_(n)  equation #16

The goal-weighting matrix 96 (“Q”) is a positive semi-definite symmetricmatrix, which includes weights on enabled goals, with higher weightscorresponding to higher priority goals. The elements of Δyr_nom and Δyrare elements of the larger vectors x_bpe and x2, respectively. Thex2-weighting matrix 97 (“R”) is a positive definite symmetric matrix andcorresponds to weights on x2. The weight on x2 is optional, but may beused to reduce sensitivity to model errors in CE and in the mathematicalmodel 22.

The optimization problem of equation #11 can be related to basepointestimator requirements by considering how the problem simplifies whengref=I and glim=I, where “I” is an identity matrix of dimensionsdetermined by context. This may be only explanatory in that if the gainmatrices 84 (“gref”) and 88 (“glim”) have these values, a change inreference values 44 (“yr”) and free basepoint values 46 (“bpf”) may beabrupt when limits switch between being active and inactive.

In this simplified case, the optimization problem of equation #11 may beminimized by #17, subject to the constraints of equations #18-20, asshown below.

$\begin{matrix}{{PI} = {\frac{1}{2}{\left( {{y\; r} - {yref}} \right)_{n + 1}}_{Q}^{2}}} & {{equation}\mspace{14mu}\#\; 17}\end{matrix}$ŷcb_(n+1)≦Y max  equation #18ŷcb _(n+1) =ŷcb _(n) +J·x2+Δ ycb _(n+1)  equation #19yr _(n+1) =yr _(n) +[I 0 0]·x2  equation #20

This is explanatory in that equations #17-19 are a mathematicalexpression of the basepoint estimator 16 requirement of making theinternal reference value 44 (“yr”) as close to yref as possible(equation #17) while meeting a predetermined quantity of limits(equation #18). In one example, the predetermined quantity of limitscorresponds to all received and enabled limits. This basepoint estimatordesign varies x2 to achieve this requirement, and equations #19-20indicate how x2 variations affect the limits and goals, respectively.

Using values between “0” and “1” for the gain matrices 84, 88 allows acontrol system designer to relax this basepoint estimator 16 requirementof equations 17-18 for brief transients as limits change between beingactive and inactive. This enables the basepoint estimator 16 to be lesssensitive to model errors, and to provide a smoother response.

Equations 11 through 14 specify a QP problem, which can be solved usinga variety of known methods and software. Equations 11 through 14 can beput into a standard QP form as follows:

$\begin{matrix}{{PI} = {{\frac{1}{2}x\; 2^{T}{H \cdot x}\; 2} - {x\; 2^{T}f}}} & {{equation}\mspace{14mu}\#\; 21}\end{matrix}$J·x2≦K  equation #22[C1 C2 C3]·x2=[C1 C2 C3]·x _(—) bpe  equation #23

Equations #24-25, shown below, define H and f.

$\begin{matrix}{H = {{\begin{bmatrix}I \\0 \\0\end{bmatrix} \cdot Q \cdot \left\lbrack {I\mspace{14mu} 0\mspace{14mu} 0} \right\rbrack} + R}} & {{equation}\mspace{14mu}\#\; 24} \\{f = {\begin{bmatrix}I \\0 \\0\end{bmatrix} \cdot Q \cdot \left\lbrack {I\mspace{14mu} 0\mspace{14mu} 0} \right\rbrack \cdot {x\_ bpe}}} & {{equation}\mspace{14mu}\#\; 25}\end{matrix}$

Two possible strategies for solving QP problems are the active setmethod and the interior point method. In the active set method, a set ofactive limits is explicitly determined. In the interior point method,the active set is only implicitly determined. A limit can be inferred tobe active when an associated “adjoint” variable or “slack” variablecrosses certain thresholds. To improve understanding, all strategies aresaid to determine an active set here, although those skilled in the artwould know that some strategies only implicitly do so.

The BPE may be set up so that x2=x_bpe when no limits are active. Thoseskilled in control theory, linear algebra, and optimization would knowhow to configure the control system and the weights to make this so.

Those so skilled will also known that when a limit is active, thesolution of the QP problem will relax a yr degree of freedom, allowingit to differ from the corresponding yref degree of freedom. If twolimits are active, two degrees of freedom will be relaxed, and so on. Ingeneral, all the yr values will relax away from all the correspondingyref values when a limit is reached. Goals with higher weights willusually be relaxed less, and those with lower weights will usually berelaxed more. Thus by selecting the weights in Q, the designer issetting the relative priorities of the goals. The mathematics ofoptimization shows that when viewed from an abstract coordinate system,rotated with respect to the natural one, a single goal degree of freedomis relaxed for each active limit. This goal degree of freedom willinvolve each of the goals to some degree, depending on the modelmatrices CE and J and on the weighting matrices Q and R.

Referring to FIG. 4, a first module 90 receives the desired change inbasepoint values 66 (“x_bpe”), mathematical model matrices 76 (“CE”) and78 (“J”) of sensitivity values, and processed limits 80 (“K”), andcalculates an initial active set of limits 92 a (“ia_(initial)”) and aslack variable 94 (“t_feas”) in response to those inputs according toequation #24 shown below (using the notation of the common Matlab®program).[ia,t _(—) feas]=min(0,K−[0 0 1]*x _(—) bpe)  equation #26

In the art of constrained optimization, t_feas is referred to as a slackvariable. The use of t_feas in the basepoint solver 74 is consistentwith the “Big K” and “Big M” techniques. The “Big K” and “Big M” referto large weights on a slack variable

From the initial active set of limits 92 a, a goal-weighting module 95selectively determines goal weighting matrix 96 which includes arelative priority for each of the plurality of goals 12, such that thegoals 12 may be prioritized according to a relative goal prioritizationscheme. In the relative goal prioritization scheme, each goal isassigned a priority or “weight” indicating its importance, and the goalsare permitted to deviate from their corresponding desired goal values.The goal-weighting module 95 also determines weighting matrix 97 for theactual changes in basepoint values 70.

The second module 98 receives the weighting matrices 96 and 97, activelimits 92 b, processed limits 80 (“K”), and matrices 76 (“CE”) and 78(“J”) as inputs and calculates the actual change in basepoint values 70a (“x2_(i)”) and an updated slack variable 100 a (“t2_(i)”) in responseto the inputs, assuming the active limits 92 b should be active.However, this assumption that the limits are active may not always betrue. By setting t2_(i)=0, the second module 98 has implicitlydetermined the values of x2_(i) and t2_(i) in the limit as the Big K andBig M weights go to infinity. This is known as the infinity K approach.

The next steps are to determine if any presumed active limits should bedropped from the active set, and if any limits implicitly presumed to beinactive should be added. The basepoint solver 74 determines if anyactive limits should be dropped from the active set 92 (step 106). Aratio 104 (“λ”) of the change in PI to a change in a limited variable iis used to determine if any limits can be dropped (step 106), and anupdated active set 92 c (“ia”) is prepared.

A scale back operation 108 performs two steps. First, the scale backoperation 108 determines if a limit should be added to the active set,as limits may be exceeded if incorrectly omitted from the active set.Second, values of actual change in basepoint values 70 a (“x2_(i)”) andthe updated slack variable 100 a (“t2_(i)”) may be scaled back (step108) if necessary to produce scaled back basepoint values 70 c (“x2”)and a scaled back slack variable 100 c (“t2”) to avoid exceeding limitsthat are not assumed to be active (i.e. not included in is 92 b). Thescale back step 108 may use initial values of x_bpe and t_feas (for afirst iteration), or may use last pass values of 100 c (“t2”) and 70 c(“x2”) for subsequent iterations, to form 100 b (“t2_(f)”) and 70 b(“x2_(f)”). Basepoint value 70 may be scaled back toward t2_(f) andx2_(f) until all limits are satisfied. The most binding limit could thenbe added to the active set. The basepoint solver 74 is thus able toiterate (step 109) and iteratively solve for the active set 92 b (“ia”).If no limits need to be added or dropped, the search for the active setis complete, and the value of x2 meets all limits and is output back tothe greater basepoint estimator 16. A description of one example ofquadratic programming, the Big K and Big M techniques, and scale backoperation can be found in “Numerical Optimization” by J. Nocedal and S.Wright (Springer-Verlag 1999).

The following is one example of a basepoint estimator application. Onemay partition y into two parts: yg for feedback signals to improve goalresponse, and yc to improve limit accuracy. One may then similarlypartition yb into ygb and ycb. The basepoint estimator 16 may then beapplied to a system with 6 states, 4 actuator signals, and 4 goaloutputs and 30 limits. The set {xb,ub,ygb, ycb} will then include 44values. Of the 6 states, 2 may be states of the controlled system 32 (or“plant states”) and 4 may be actuator states. Of the 4 goal feedbacksignals, ygfb, 2 may be from sensors measuring plant variables, and 2may be simply basepoints of two of the actuators. The latter two signalsare from within the controller.

In this application, there are four reference values: two may beassociated with two plant feedback measurements and two may beassociated with the two actuator basepoints included in yg. All 30limits may have elements in feedback vector yc: 22 are from feedbacksensors on the plant and 8 are from the actuator model implemented inthe controller. Of the 30 limits, 4 may be maximums and minimums of thetwo plant state values, 8 may be maximums and minimums of the fouractuator output values, and 18 may be otherwise. In this applicationexample, there are 18 dependencies between the 44 basepoint values: 4 ofxb that may be bases for actuator states are equal to the 4 actuatorbase values in ub, 2 in ygb that may be actuator bases are equal to the2 associated actuator bases in ub, 2 in ygb that may be state bases areequal to the associated 2 state base values in xb, 4 elements in ycb maybe plus and minus the bases for two plant states and may be equal to theassociated values in ±xb, and 8 in ycb may be plus and minus bases for 4actuators and may be equal to the associated ±ub values.

The 18 dependencies reduce the 44 basepoints to 26 that are independentvalues to be estimated. These 26 may be grouped into ycb, bpf, and yr asthe following: ycb may include bases for 18 of the limits that are otherthan states and actuators, yr may include 4 bases for 2 of the 4 plantvariables measured by feedback sensors and 2 actuator base values, andbpf may include 4 bases including 2 plant states and the 2 actuatorbases not included in yr.

Although a preferred embodiment of this invention has been disclosed, aworker of ordinary skill in this art would recognize that certainmodifications would come within the scope of this invention. For thatreason, the following claims should be studied to determine the truescope and content of this invention.

1. A method, comprising: receiving a plurality of goals, wherein eachgoal has a desired value; receiving a plurality of sensor feedbacksignals from a controlled system; receiving a plurality of predictedoutput values of the controlled system from a mathematical model;estimating on a microprocessor a desired change for a plurality ofbasepoint values in response to the goals, the feedback, and thepredicted output values; calculating on the microprocessor an actualchange in basepoint values in response to a plurality of limits and thedesired change for the plurality of basepoint values according to aplurality of goal weights while holding limits, wherein the plurality ofgoal weights include a relative priority for each of the plurality ofgoals according to a relative goal prioritization scheme; combining onthe microprocessor the actual change in basepoint values with last passvalues of the plurality of basepoint values to produce an updatedbasepoint estimate; and transmitting actuator requests to the controlledsystem in response to the updated basepoint estimate, wherein theactuator requests effect change in the controlled system.
 2. The methodof claim 1, wherein said step of calculating on the microprocessor anactual change in basepoint values in response to a plurality of limitsand the desired change for the plurality of basepoint values accordingto a plurality of goal weights while holding limits includes: receivingthe plurality of limits; receiving a plurality of matrices from themathematical model, wherein one of the matrices is a goal-weightingmatrix that includes the plurality of goal weights; receiving theplurality of desired changes for the plurality of basepoint values;formulating a constrained optimization problem that minimizes adifference between the actual changes in basepoint values and thedesired change in basepoint values, and that ensures all limits are met;and solving the constrained optimization problem to determine updatedactual changes in basepoint values in response to the desired changes,the goal-weighting matrices, and the limits.
 3. The method of claim 2,further comprising: defining the goal weighting matrix to include arelative priority for each of the plurality of goals; and defining abasepoint weighting matrix for the actual changes in basepoint values.4. The method of claim 3, wherein said step of formulating a constrainedoptimization problem includes: defining a performance index to includelinear terms and quadratic terms; and defining a linear approximation ofthe mathematical model to relate the actual changes in basepoint valuesto a plurality of limited variables.
 5. The method of claim 2, whereinsaid step of solving the constrained optimization problem to determineupdated actual changes in basepoint values is implemented using aquadratic programming algorithm.
 6. The method of claim 5, wherein thequadratic programming algorithm includes at least one of a Big Mtechnique or a Big K technique.
 7. The method of claim 6, wherein saidat least one of the Big M technique or the Big K technique is modifiedto be a infinite K technique.
 8. The method of claim 1, wherein a highergoal weight corresponds to a higher priority.
 9. The method of claim 1,wherein said step of calculating an actual change in basepoint valuesmaintains feedback dynamic properties of an estimator loop.
 10. Themethod of claim 1, wherein said step of receiving a plurality ofpredicted output values includes: creating a mathematical model topredict behavior of the controlled system; and mapping the actual changein basepoint values into a format that may be processed by themathematical model.
 11. The method of claim 1, wherein the mathematicalmodel is a time varying linear model.
 12. The method of claim 11,wherein the mathematical model is a quasi-linear parameter varyingmodel.
 13. The method of claim 2, further comprising: using the matricesfrom the mathematical model to maintain desirable dynamics throughout acontrolled system operating envelope and across various permutations ofactive limits.
 14. The method of claim 1, further comprising: using afirst gain matrix to provide a smooth transition off of a limit.
 15. Themethod of claim 14, further comprising: using a second gain matrix toprovide a smooth transition onto a limit.
 16. The method of claim 1,further comprising: creating actuator requests for the controlled systemin response to the updated basepoint estimate.